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24 November 2020
  » arxiv » 0911.1215

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Stability properties of periodically driven overdamped pendula and their physical implications
Jukka Isohätälä ; Kirill N. Alekseev ;
Date 6 Nov 2009
AbstractWe consider the first order differential equation with a sinusoidal nonlinearity and periodic time dependence, that is, the periodically driven overdamped pendulum. The problem is studied in the case that the explicit time-dependence has symmetries common to pure ac-driven systems. The only bifurcation that exists in the system is an exchange of stability between two symmetric nonlinear modes. Using a type of Prufer transform to a pair of linear differential equations, we derive an approximate condition of the bifurcation. This approximation is in very good agreement with our numerical data. In particular, it works well in the limit of large drive amplitudes and low external frequencies. We demonstrate the usefulness of the theory applying it to the models of ac-driven semiconductor superlattices and Josephson junctions.
Source arXiv, 0911.1215
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